从理论上分析了颗粒流本构关系的最一般形式，及其在平面简单剪切流这一典型且常用的剪切流动条件下的本构关系。颗粒群受剪从极慢颗粒流动，低速颗粒流动，一直到快速颗粒流动的本构关系可以统一起来。利用试验资料，对颗粒在空气中受剪的本构关系进行了分析，很好地验证了理论分析结果。尤其是，理论分析及所有试验都表明在正应力和剪切应力表达式中存在流速梯度的线性项，揭示出在颗粒流中还存在颗粒的相对滑动及相互挤压作用，该项与普通流体的线性粘滞应力类似，但有根本的不同。

Starting with the kinetic theory for dilute solid/liquid two-phase flow, a mathematical model is established to predict the flow in a horizontal square pipe and the predictions are compared with LDV measurements. The present model predicts correctly two types of patterns of the vertical distribution of particle concentration observed in experiments, and also gives different patterns of the distribution of particle fluctuating energy. In the core region of the pipe, the predicted mean velocity of particles is smaller than that of liquid, but near the pipe bottom the reverse case occurs. In addition, full attention is paid to the mechanism for the vertical distribution of the average properties of particles such as concentration and mean velocity. From the kinetic-theory point of view, the cause of formation for different patterns of the vertical concentration distribution is not only related to the lift force exerted on a particle, but also related to the distribution of particle fluctuating energy.

On the basis of traditional particle-in-cell methods, a particle model has been developed to simulate flow over large areas. Under the assumption that the fluid medium is an assembly of many small, independent fluid particles, the momentum equation for a particle is derived for shallow-flow conditions. In the formulation used, only two forces are involved. One is the hydrostatic force arising from the accumulation of different numbers of particles at different locations. The other is a friction force that varies inversely with flow depth and quadratically with particle velocity and bed roughness. The velocity and spatial positions of all particles are averaged at fixed grid points to obtain the overall flow behavior. The particle model is demonstrated through an application to a documented 1954 flood in the Jingjiang River flood diversion area in Hubei, China. The flood lasted 300 h, with the total discharge volume being 4 billion m3. Good agreement between computed and observed water levels was obtained. Convergence of the method is demonstrated by repeatedly doubling the number of particles employed in the computation until there is little change between simulations.